The field of the invention relates to the problem of rejecting exogenous disturbances acting on dynamical systems (or "plants"). In particular, the invention pertains to a method and system for noise and vibration suppression that does not require measurement of the actual disturbance.
Heretofore, several methods required a priori knowledge of the spectral characteristics of the disturbance in addition to models of all four paths in the plant including actuators and sensors shown in FIG. 1, that is, G.sub.zw (the "primary path"), G.sub.zu (the "secondary path"), G.sub.yw (the "reference path") and G.sub.yu (the "feedback path"). These methods are described in reference 5 of the appended listing of references. Other methods used for active noise control described in references 1, 2, 6 through 12, do not require knowledge about the disturbance but often require a direct measurement of it, and require an FIR (finite impulse response) or IIR (infinite impulse response) model of G.sub.zu. These methods use instantaneous measurements for adaptation and do not accurately characterize the effect of the control over a window of time.
Despite the need for a method and system that can adapt based on retrospective information obtained from sensors to account for the effect of the system and method over a window of time, none was known. Thus, there was the need for a method and system using a retrospective performance evaluation in a special heretofore unknown form. A need also existed to determine an explicit step size or well-defined distance based upon the retrospective performance evaluation.
The disclosed method and system of this invention is applicable to a wide class of disturbance rejection problems, including but not limited to active noise and vibration control. Other applications include command-tracking in which the command is viewed as a disturbance signal whose effect is rejected in the output error signal.
The present method does not require knowledge of the disturbance spectrum nor a measurement of it, and only requires the numerator of the ARMARKOV model G.sub.zu denoted by the Toeplitz matrix B.sub.zu.
The present method uses ARMARKOV models to describe the plant including sensors and actuators as well as the disturbance rejection controller. These models are described below.